IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00625669.html
   My bibliography  Save this paper

Price dynamics on a stock market with asymmetric information

Author

Listed:
  • Bernard de Meyer

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

When two asymmetrically informed risk-neutral agents repeatedly exchange a risky asset for numéraire, they are essentially playing an n-times repeated zero-sum game of incomplete information. In this setting, the price Lq at period q can be defined as the expected liquidation value of the risky asset given players' past moves. This paper indicates that the asymptotics of this price process at equilibrium, as n goes to ∞, is completely independent of the "natural" trading mechanism used at each round: it converges, as n increases, to a Continuous Martingale of Maximal Variation. This martingale class thus provides natural dynamics that could be used in financial econometrics. It contains in particular Black and Scholes' dynamics. We also prove here a mathematical theorem on the asymptotics of martingales of maximal M-variation, extending Mertens and Zamir's paper on the maximal L1-variation of a bounded martingale.

Suggested Citation

  • Bernard de Meyer, 2010. "Price dynamics on a stock market with asymmetric information," Post-Print hal-00625669, HAL.
    • Handle: RePEc:hal:journl:hal-00625669
    DOI: 10.1016/j.geb.2010.01.011
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    3. Fedor Sandomirskiy, 2014. "Repeated games of incomplete information with large sets of states," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 767-789, November.
    4. Fedor Sandomirskiy, 2018. "On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values," Dynamic Games and Applications, Springer, vol. 8(1), pages 180-198, March.
    5. Bernard de Meyer & Moussa Dabo, 2019. "The CMMV Pricing Model in Practice," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02383135, HAL.
    6. Shino Takayama, 2013. "Price Manipulation, Dynamic Informed Trading and Tame Equilibria: Theory and Computation," Discussion Papers Series 492, School of Economics, University of Queensland, Australia.
    7. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2018. "Belief-free price formation," Journal of Financial Economics, Elsevier, vol. 127(2), pages 342-365.
    8. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
    9. Takayama, Shino, 2021. "Price manipulation, dynamic informed trading, and the uniqueness of equilibrium in sequential trading," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    10. Pierre Cardaliaguet & Catherine Rainer, 2012. "Games with Incomplete Information in Continuous Time and for Continuous Types," Dynamic Games and Applications, Springer, vol. 2(2), pages 206-227, June.
    11. Bernard De Meyer & Gaëtan Fournier, 2015. "Price dynamics on a risk averse market with asymmetric information," Documents de travail du Centre d'Economie de la Sorbonne 15054, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. Shino Takayama, 2018. "Price Manipulation, Dynamic Informed Trading and Tame Equilibria: Theory and Computation," Discussion Papers Series 603, School of Economics, University of Queensland, Australia.
    13. Fabien Gensbittel, 2015. "Extensions of the Cav( u ) Theorem for Repeated Games with Incomplete Information on One Side," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 80-104, February.
    14. Bernard de Meyer & Moussa Dabo, 2019. "The CMMV Pricing Model in Practice," Post-Print halshs-02383135, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00625669. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.